The Matrix Riccati Equation and the Noncontrollable Linear-Quadratic Problem with Terminal Constraints
Pavol Brunovský, Jozef Komorník · SIAM Journal on Control and Optimization · 1983
It is proved that each positive semidefinite symmetric solution of the matrix Riccati equation corresponds to an optimal control problem with suitable terminal cost and constraints. The approximation scheme for the computation and characterization of the optimal cost and optimal controls of the problem with terminal constraints is extended to the noncontrollable case.